This video shares an idea for giving students some choice in solving systems of equations, but not the typical choice of having them select their preferred strategy but instead having them choose the equations to put into the system in the first place.
Otten, S., & Otten, A. (2016.) Selecting systems of linear equations. Mathematics Teacher, 110(3), 222-226.
We teachers often follow a common sequence with regard to solving systems of equations. First, we show students a solution strategy, like graphing, elimination, or substitution, and we have them practice that strategy. So we give them a strategy and we give them systems to solve. Not much room for choice.
After they get pretty good at various strategies, we tend to allow students a bit of choice. We still give them the system to solve, but they are free to choose a strategy. This allows students to think about the strategy that is best suited for a given system … but, it may also result in students who love elimination, solving by elimination again and again. (We all have those students who prefer rigid consistency, am I right?)
The point is that we have this routine of always giving the students the system that they have to solve. We’re going to ask that you disrupt the routine by allowing students to make a different choice, the choice of which equations go into the system in the first place.
To start, identify a strategy that students will use to solve some system. Let’s say elimination. Then, give them not systems but a list of individual equations like so. Then, ask the students to use those equations to create their own system that they will solve.
By giving them this choice, you’ll notice that students will begin to focus on the structure of the equations in relation to the strategy. In the prior example, students might look for equations already in standard form. That’s a nice thing for them to notice, and it helps make it more relevant that they’ve learned about different forms of linear equations.
Other students may focus even more narrowly on the terms in the equations, looking for terms that will cancel. This shows great insight into the overarching goal of the elimination method. Because students have choice, you will likely have different students selecting different systems for the same strategy. This creates some rich opportunities for discussions of why they chose what they did and allows students to generalize across their various choices. For even more discussion, you could ask students to create a system they would not want to solve using the given strategy. This allows them to think about when not to use a strategy, which is just as important as knowing when to use it.